How do mission designers know at what angle to land on an astronomical body such as the Moon, Mars, or Earth?

Comparing typical trajectories for Mars (red), Earth (blue), and Venus (yellow) during the descent from an altitude of nearly 20 miles (32 kilometers) to the surface of the planet shows how an atmosphere's thickness affects the landing angle. // Astronomy: Roen Kelly, after John Anderson

A planetary body’s atmosphere controls the angle during entry, descent, and landing from a combination of the gravitational force and atmospheric drag. Venus and Earth have thick atmospheres, so drag slows the entry capsule to the point where it falls straight down to the surface the last few miles. For Earth, this vertical descent occurs at an altitude of about 6 miles (10 kilometers), while for Venus, with its much thicker atmosphere, it occurs at about 35 miles (60km). A craft will deploy parachutes to provide a soft landing — not to control the angle.

The atmosphere of Mars, however, is so thin that vertical descent never occurs. The Mars Exploration Rover Opportunity experienced a perfect example of this in 2004: A parachute deployed at an altitude of about 4.7 miles (7.5km) to slow the entry capsule for a softer landing, but this equipment had little effect on the landing angle. The Mars Science Laboratory landing on August 6, 2012, incorporated a guidance system for a vertical touchdown to place the Curiosity rover softly on the surface.

Because the Moon has no atmosphere, all lunar landings depend on guidance rockets; one example of this process is Neil Armstrong’s heroic manual guidance of the Apollo 11 Lunar Module Eagle on July 20, 1969.